Well, the Organians pretty much did that: purely pacifistic and illusory aliens who used their heretofore unknown powers to stop a war between the Federation and the Klingons forcibly and without their consent. The Halkans wouldn't have had to be any different were the circumstances similar.
But the Organians weren't really pacifists, they just wanted to be left alone. They found the presence of corporeal beings intolerable, so they forced the peace in order to get the noisy kids off their lawn.
I think that the big differences between what we saw in Yesteryear/Yesterday's Enterprise/Parallels/Kelvinverse is that they all (with the exception of Parallels) diverged from the Prime timeline relatively close to the time period of the shows and dealt with time travel from the Prime timeline creating them.
But they all diverged decades earlier, which is enough to make it unlikely that the same people would end up on the same ship at the same time, especially if their life circumstances were very different.
Parallels stands out as it deals with actual parallel universes
A meaningless distinction. Fiction uses "parallel universe," "alternate timeline," and other such terms interchangeably, and from a physics standpoint, they're all just alternative quantum measurement histories, superposed solutions to the Schroedinger equation of the universe, with no meaningful physical difference between one created by time travel and one arising through a spontaneous branching. (Indeed, strictly speaking, alternate quantum timelines can
only be created by quantum-scale events, not by macroscopic events like time travelers' actions, so it's more likely that any parallel timeline resulting from time travel was one that spontaneously branched off just before the time travelers arrived, giving them the opportunity to make it happen differently.)
If anything were actually, literally a separate universe, rather than an alternate history of our universe, then it wouldn't have Earth or humans or Starfleet or anything we recognize. It would just be a different physical place with a completely separate evolution, with different worlds and species and history altogether. You wouldn't find a goateed copy of yourself or an Earth where Hitler won any more than you'd find a duplicate Manhattan Island or Nile River on a planet of Alpha Centauri. It's just a separate place, not a duplicate of the place we come from. Anything that has Earth and humans and recognizable individuals in it can
only be an alternate history, no matter what terminology the story uses.
And don't give me the "Well, there's an infinite number of universes so some of them just coincidentally happen to match ours" argument, like they do in the IDW Kelvin comics. That's an abuse of the concept of infinity. If there is an infinite number of universes, then the probability of interacting with one that coincidentally duplicates ours is the reciprocal of infinity, which is zero. It would take an infinite amount of time to find one and thus it would never happen.
The Mirror Universe differs drastically in that the apparent point of divergence was thousands of years ago.
I'm not convinced of that. Dictatorial regimes aren't above rewriting their history to fit state ideology. It's possible the divergence point was more recent but the Empire rewrote its history and literature to make it seem like the divergence was further back.
As for the photosensitivity thing, that makes no sense, since we saw no sign of it in "Mirror, Mirror" or DS9. So it must only apply to a certain percentage of the Terran Empire population, maybe the result of a botched eugenics experiment. Georgiou's claim that it applied to all Mirror humans would just be one more bit of state-approved revisionism.
That begs the question though, was it only human history that diverged and thus altered galactic history? Is it only the Terrans who were materially different from their Prime counterparts (being photosensitive and culturally barbaric) prior to Mirror First Contact?
Clearly yes. Every change we've seen in other species can be attributed to their conquest by or war against the Terran Empire. Vulcans are still logical, just more ruthless because they've had to be to survive. Other races are much the same except in the way their history has played out differently under Terran influence, for instance, Bajor being conquered by the Empire first and allying with Cardassia against it.
I always like to imagine every universe has its own mirror universe in which the morality is inverted and who does/doesn't have a goatee is switched.
Again, the MU was never supposed to be a world where
everyone's morality was inverted -- the Halkans were the same, Spock was ultimately the same underneath, etc. The title "Mirror, Mirror" doesn't refer to simple reversal -- it's from "Snow White," the incantation to the magic mirror that reveals the unvarnished truth. The point wasn't "These are our complete opposites," it was "their savagery is inside us too."